Decoherence induced by an interacting spin environment in the transition from integrability to chaos

We investigate the decoherence properties of a central system composed of two spins 12 in contact with a spin bath. The dynamical regime of the bath ranges from a fully integrable limit to complete chaoticity. We show that the dynamical regime of the bath determines the efficiency of the decoherence process. For perturbative regimes, the integrable limit provides stronger decoherence, while in the strong coupling regime the chaotic limit becomes more efficient. We also show that the decoherence time behaves in a similar way. On the contrary, the rate of decay of magnitudes like linear entropy or fidelity does not depend on the dynamical regime of the bath. We interpret the latter results as due to a comparable complexity of the Hamiltonian for both the integrable and the fully chaotic limits.